SCIENCE FILE / An exploration of issues and trends affecting science, medicine and the environment | MIND OVER MATTER

For Mathematicians, 'a Once in a Century Thing'

Mathematics has a strange gift. It is "unreasonably effective" in places where it has no right to be. Like a hammer that turns out to be good at scrambling eggs, or a basketball star who decides to become a rapper. Math plays a starring role not only in fields where you might expect it--say, physics--but also unlikely places such as Hollywood filmmaking, ecology, medicine, traffic control.

What's a nice equation like you doing in a place like that?

This week, the superstars of mathematics are gathering at UCLA to celebrate this strange flowering, as well as look for fertile ground to plant new fruit. It is a gathering the likes of which has not been seen for at least 100 years, with the equivalent of nearly a dozen Nobel laureates. (Math has no such thing as a Nobel Prize, but other honors are considered to confer a similar status within the field.)

"Woodstock" is the closest comparison UCLA math chair Tony Chan could come up with. "It's a once in a century thing."

The official occasion is the hundredth anniversary of a famous lecture given by the great mathematician David Hilbert at an international meeting in Paris in 1900. Hilbert set out the 23 most important questions facing mathematicians of his day--thereby setting the agenda, more or less, for the century to come.

The meeting running this week (Aug. 6 through 12) at UCLA hopes to do the same.

The range of subjects these rock stars of mathematics are addressing is staggering: the mathematics of thinking and subatomic particles, of species and ecosystems, computing and climate change, financial markets and materials, the creation of virtual worlds and the decoding of the human genome.

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How does math do it? What is it about this strange hieroglyphics of numbers and symbols that allows it to spread its tentacles through so many disparate fields, holding up the foundation of everything from astronomy to human perception?

"Nobody quite knows," said Chan. "That's why they call its effectiveness unreasonable. People have been trying to explain it [for a long time]. They cannot."

One key is that math describes everything because it describes nothing. It is an abstraction so extreme that in its pure form, it has nothing to do with the real world. The glory of mathematics, as the late Caltech physicist Richard Feynman put it, "is that we do not have to say what we are talking about." Or as the mathematician Bertrand Russell famously put it: "Mathematics may be defined as the subject in which we never know what we are talking about, or whether what we are saying is true."

Because math isn't stuck in any single context, it is endlessly versatile--like letters of the alphabet, equally adept at writing sonnets or advertisements. Its ability to distill the essence is what makes it universal--like love or hate.

Curiously, however, most math doesn't start out as abstract. Often, it grows out of something very concrete, an attempt to understand some puzzling aspect of the physical world--say, Newton's attempt to understand gravity, which led to calculus.

But then, something strange happens. The abstracted patterns take on a life of their own. "At that point, it becomes mathematics," said Chan.

It can take a while for the math to settle, digest, mature. When it does, the universality of its applications surprises almost everyone. Like the first crude wheel that evolved into cars and trains, ball bearings and salad spinners, roller-blades and yo-yos, navel rings and "Wheel of Fortune"?

And that blossoming into unexpected forms is precisely what mathematicians think is happening again today and what they intend to celebrate--and build upon--at the conference.

The university will also be dedicating its new Institute for Pure and Applied Mathematics, one of only three such National Science Foundation-funded centers in the country. "This puts us on the map," said Chan. Previously, people from the East Coast or abroad equated math on the West Coast with UC Berkeley, he said. With the institute, UCLA becomes a real player. Needless to say, all this is music to the mathematicians' ears. And this week at UCLA, it's time to rock 'n roll.

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Information about the conference and related events can be found at: http://www.math.ucla.edu/newsevents/news/ams2000.html